Solve (x-5)^2=-11

$$( x - 5 ) ^ { 2 } = - 11$$

Solve for x (complex solution)

$$x=-\sqrt{11}i+5\approx 5-3.31662479i$$

$$x=5+\sqrt{11}i\approx 5+3.31662479i$$

Steps by Finding Square Root

Add 5 to both sides of the equation.

$$x-5-\left(-5\right)=\sqrt{11}i-\left(-5\right) x-5-\left(-5\right)=-\sqrt{11}i-\left(-5\right)$$

Subtracting -5 from itself leaves 0.

$$x=\sqrt{11}i-\left(-5\right) x=-\sqrt{11}i-\left(-5\right)$$

Subtract -5 from i\sqrt{11}.

$$x=5+\sqrt{11}i$$

Subtract -5 from -i\sqrt{11}.

$$x=-\sqrt{11}i+5$$

The equation is now solved.

$$x=5+\sqrt{11}i x=-\sqrt{11}i+5$$